Modern Atomic Theory-Electronic Structure of Atoms

DR HNIMIR-CH7

Problems with the atomic model?Where should (-) electrons be found?

First, a Little About Electromagnetic Radiation- Waves

Another Look

Relationship

λλλλ νννν = c

Planck’s Relationshipblack body radiation experiment

∆E = h ν

ProblemFor green visible light of wavelength 486 nm

a. what is the frequency of this radiation?

b. Calculate ∆E

λλλλ νννν = c

∆E = h ν

Meaning of results?

4.086x10-19 J is the minmum amount of energy to be gotten from this green light. If you want more,

you have to take 2 x 4.086x10-19 J (or 3x, 4x, etc)

4.086x10-19 J

green light of wavelength 486.0 nm comes "packaged" in packets

(called quanta in general and photons for EM) of 4.086x10-19 J

Two More ThingsFor red light of wavelength 725.0 nm

∆E is 2.740x10-19J

2.740x10-19J

When you calculate ∆E the units are actually J/photon

The EM Spectrum

Einstein’s Involvement

"particle / wave dualism"

The Photoelectric Effect

Frauhoffer LinesWith good optics it was noticed that

the continuous spectrum obtained from the sunhad very fine black lines in it

Line SpectraThe Bohr Atom

The Hydrogen Spectrum

The Bohr ModelNiels Bohr interprets the lines as quantized energy emitted by electrons between allowed energy levels

1

2

3

4

an electron absorbs energy and is promoted to

a higher energy level

1

2

3

4

the excited electron returns to a lower energy level and emits a specific amount of energyseen as a sharp line of light

1

2

3

4

∆E

Bohr Orbits

Bohr calculates the energy of the nth orbit by the formula

En = -B

n2

where B= 2.180x10-18J for the hydrogen atom

ProblemCalculate the energy of the 2nd and 4th energy levels

En = -2.180x10-18J

n2

Calculate ∆∆∆∆E for the transition (∆∆∆∆E= E2-E4)

Calculate the Wavelength (in nm) Associated with the Answer from

the Last Slide∆E= - 4.087x10-19J

∆E = h νλλλλ νννν = c

Interpretation of the Last Slide’s Results

λλλλ= 486.0 nm

700 nm600 nm500 nm400 nm

This spectral line is due to a 4 2 electron transition

A Useful Derived Equation∆E= Efinal - Einitial = Einner - Eouter

-2.180x10-18J

ni2

-2.180x10-18J

no2

∆E= -

Redo the previous problem using this equation

1

ni2

1 no

2∆E= -2.180x10-18J

Regions of Spectral Lines

1

2

3

4

UV

Lyman series

1

2

3

4

VIS

Balmer series

1

2

3

4

IR

Paschen series

DeBroglieAssumes that if light (waves) could have par ticle proper ties

then particles could have wave properties

∆E = h ν∆E = mc2

h ν= mc2 h c = mc2

λ λ = h mc

InterpretationThe wavelength of an electron must be

an integer multiple of the Bohr orbits (quantized)

Evidence for Wave Nature of the Electron

Interference Patterns Observed

Heisenberg Uncertainty Principle

Schroedinger’s Equation

He combines the mathematics of waves and probability

He constructs 3D probability maps for electrons, called " orbitals"

Orbitals

"s""p"

s,p and d orbitals

Energy Levels, Sub-levels and Orbitals

ENERGY

1

2

3

4

energy level sub-level

1s

2s

2p

3s

3p

3d

4s4p4d4f

orbitals

Electron Configurations-putting it all together

O8 8 electrons

start with the lowest energy level 1s sublevel is only one in 1st energy levelthe one orbital can hold 2 electrons

this fills the first energy level

next electrons goes in the 2nd energy levelthe s sub-level is lower than ptwo electrons fill the s sublevel

there is a p sublevel in the 2nd energy level

the remaining electrons can go into the p sub-level of the 2nd energy level

Order of electron filling-first 36 elements (through krypton)

1 s 2 s 2 p 3 s 3 p 4 s 3 d 4 p

“Out of Order”

3s

3p

3d

3rd energy level

4th energy level

4s

4p4d4f

4s

4p4d4f

3s

3p

3d

3rd energy level

Maximum number of electrons:

1 s 2 s 2 p 3 s 3 p 4 s 3 d 4 p

Simplifying Electron Configurations

"inert gas core" notation

19K

Electron Spin-Stern Gerlach Experiment

furnace

Agbeam of gaseous

silver atoms

N

S

powerful magnet

Electron Spin Pairing

representing paired electrons in an energy diagram

Energy Diagrams- visualizingelectron configurations

1s 2s 2p

1s

2s 2p

Example-carbon

1s

2s 2p

6C 1s2 2s2 2p2

Q5Write electron configurations for Si and Ge

Q5 cont.Construct energy diagrams for P and F

Q5 cont.

Transition Metals

Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn

4s

3d

2 2 2 2 2 2 2 2 2

0 1 2 3 5 6 7 8 10

1

5

1

10

Why the difference?

Half-filled Sub-levels are More Stable

4s3d

Problemdo the same for Cu

4s3d

Magnetic Properties of Atoms

Quantum Numbers

Principle Q.N.n

n gives the energy level of the electron

n = 1,2,3,.... (any integer)

Angular Momentum Q.N.l

the values of l are:

0, 1, ...., n-1

gives the number of sublevels in any energy level

(if n =2, then l= 0 and 1)

meaning:in the second energy level (n=2) there are two sub-levels (s and p)

l sub-level

0 s

1 p

2 d

3 f

Orientation Quantum Numberml

gives the number of orbitals in a sublevel

ml = -l ....,0,.... +l

if l = 1 (p sub-level)

ml = -1,0,+1 (three p orbitals in the p sub-level)

Spin Quantum Numberms

tells whether an electron is unpaired (the first into that orbital) or paired

ml = +1/2 for the first electron in an orbital

ml = -1/2 for the paired electron

How it Works

8O 1s22s22p4

1s

2s 2p

Q6Provide the four QN's for the characteristic electron of phosphorous

Which element would have the following character isticQN's?

n = 2 l = 1 ml = 0 ms = -1/2